Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p\geq 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a nontrivial $p$-restricted irreducible tensor indecomposable rational $KG$-module such that the restriction of $V$ to $H$ is irreducible.
In this paper the authors classify the triples $(G,H,V)$ of this form, where $V \neq W,W^{*}$ and $H$ is a disconnected almost simple positive-dimensional closed subgroup of $G$ acting irreducibly on $W$. Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples $(G,H,V)$ where $G$ is a simple algebraic group over $K$, and $H$ is a maximal closed subgroup of positive dimension.
ISBN: | 9781470410469 |
Publication date: | 30th July 2015 |
Author: | Timothy C Burness, Soumaia Ghandour, Claude Marion, Donna M Testerman |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 110 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Algebraic geometry Algebra |